SSC GD Constable 2026 Official Paper (Held On 25 May, 2026 Shift 2) (Previous Year Paper)

Logic: (Previous term × 2) + 1 = Next term

 

The missing term that completes the series is 59.

Hence, the correct answer is "Option 1".

Logic followed here is.

Logic: The next term in the series is determined by multiplying the previous term by a factor (alternating between 2 and 3) and then adding 3 to the product.

Hence, the correct answer is "Option 4".

Logic followed here is:

Logic: The first letter of each term increases by 5 in each step, and the second letter of each term increases by 6 in each step according to the alphabetical order.

The missing term is IF.

Hence, the correct answer is "Option 4".

Logic followed here is:

The series consists of letter pairs where each letter follows a specific positional increment pattern independently.

Thus, the missing term is QJ.

Hence, the correct answer is "Option 1".

The logic followed in this pattern is a series of alphabetical shifts for each letter in the clusters.

For the set '(BR, EW, HB)':

For the set '(AL, DQ, GV)':

Applying the same logic to '(OV, RA, UF)':

Thus, the group (OV, RA, UF) follows the same logic.

Hence, the correct answer is 'Option 3'.

The logic followed in this pattern is a combination of alphabetical shifts and alphabetical opposites.

For the set '(FZ, CW, XD)':

For the set '(ZG, WD, DW)':

Applying the same logic to '(PS, MP, NK)':

Thus, the group that follows the same logic is (PS, MP, NK).

Hence, the correct answer is 'Option 4'.

Logic followed here is.

Logic: This is a numerical series where each subsequent term is obtained by adding a constant difference of 56 to the previous term.

 

The missing term in the series is 737.

Hence, the correct answer is "Option 2".

Logic followed here is.

According to the information given in the question, the sitting arrangement is as follows:

1. No one is sitting to the left of T: This means T is at the extreme left position (Position 1).

2. There is only one person to the right of S: This means S is at the fourth position from the left in a row of five people.

3. P and S are immediate neighbours: P could be at Position 3 or Position 5. However, another condition states that P is sitting next to B. If we place P at Position 5, there is no place for B next to it (since S is at Position 4). Therefore, P must be at Position 3 and B must be at Position 2.

4. V and T are not immediate neighbours: The only remaining position for V is Position 5. Since T is at Position 1, they are not immediate neighbours, which satisfies the condition.

Final Arrangement:

The persons sitting between T and S are B and P.

Total number of persons = 2

Hence, the correct answer is "Option 4".

Given: 7 people G, H, I, J, K, L and M are sitting around a circular table facing towards the centre (not necessarily in the same order).

 

1. M sits second to the right of J. G sits second to the right of K and second to the left of J.

 

2. I is not the immediate neighbour of J.

 

3. M is not the immediate neighbour of H.

Thus, I is sitting third to the left of J.

Hence, the correct answer is "Option 4".

Given:

KH120 : GD500

PO420 : LK800

Similarly,

JT320 : ?

Hence, JT320 is related to FP700.

Hence, the correct answer is 'Option 1'.

Given:

BKL780 : YHI540

ZMO600 : WJL360

ANP540 : ?

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: Second Number = First Number + 43

For the first pair 8439 : 8482

⇒ 8439 + 43 = 8482.

For the third pair 39 : 82

⇒ 39 + 43 = 82.

Applying the same logic to the second pair

2724 : ?

⇒ 2724 + 43 = 2767.

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = First Number − 276

For the first pair 175 : −101

⇒ 175 − 276 = −101.

For the third pair 923 : 647

⇒ 923 − 276 = 647.

Applying the same logic to the second pair

855 : ?

⇒ 855 − 276 = 579.

Hence, the correct answer is 'Option 3'.

Logic followed here is:

The series consists of two parts: an alphabetical pattern and a numerical pattern.

 

By combining the alphabetical part (IK) and the numerical part (460), we get the missing term IK460.

Hence, the correct answer is "Option 4".

The logic followed here is that each term in the series consists of three letters and a number, each following its own mathematical progression.

 

The expected fifth term based on the pattern is EQM1350. However, the given term is DPN1350.

Hence, the correct answer is "Option 2".

Concept:

The hour hand covers 360° in 12 hours.

Angular distance covered by the hour hand in 1 hour = 360 ÷ 12 = 30°

Angular distance covered by the hour hand in 1 minute = 30 ÷ 60 = 0.5°

The minute hand covers 360° in 60 minutes.

Angular distance covered by the minute hand in 1 minute = 360 ÷ 60 = 6°

Calculation:

The time is between 7 AM and 8 AM and the required angle is 150 degrees.

Let the required time be 7:M AM.

At 7:00, the hour hand is at 7 × 30 = 210° (measured from the 12 o'clock position).

Angle of the hour hand at 7:M = 210 + 0.5M

Angle of the minute hand at 7:M = 6M

The angle between the hands is the absolute difference between their angular positions:

Angle = |(210 + 0.5M) − 6M|

150 = |210 − 5.5M|

Case 1:

210 − 5.5M = 150

5.5M = 210 − 150

5.5M = 60

M = 60 ÷ 5.5 ≈ 10.91 minutes

Case 2:

210 − 5.5M = −150

5.5M = 210 + 150

5.5M = 360

M = 360 ÷ 5.5 ≈ 65.45 minutes (Since this value exceeds 60 minutes, it falls after 8 AM)

Rounding the value from Case 1 to the nearest minute, we get M ≈ 11.

Thus, the time is approximately 7:11 AM.

Alternate Method

The angle between the hour hand and minute hand is given by the formula:

$\text{Angle} = \left| \frac{60H - 11M}{2} \right|$

Where H = hours and M = minutes.

Given H = 7 and Angle = 150.

150 = |(60 × 7 − 11M) ÷ 2|

300 = |420 − 11M|

420 − 11M = 300 ⇒ 11M = 120 ⇒ M = 120 ÷ 11 ≈ 10.91

So, the time is approximately 7:11 AM.

Therefore, the correct option is 1.

Concept:

To find the time shown by the clock, we first calculate the total duration between the initial time and the target time. Then, we determine the total gain based on the given rate of error and add it to the correct time.

Calculation:

The clock shows the correct time at 5 AM.

The time duration from 5 AM to 5 PM on the same day = 12 hours.

Convert the total hours into minutes:

Total minutes = 12 × 60 = 720 minutes.

It is given that the clock gains 1 second every 5 minutes.

Total gain in 720 minutes = 720 ÷ 5

Total gain = 144 seconds.

Now, convert the gained seconds into minutes and seconds:

144 seconds = (120 + 24) seconds

Since 60 seconds = 1 minute, 120 seconds = 2 minutes.

So, Total gain = 2 minutes and 24 seconds.

The correct time is 5 PM. Since the clock is gaining time, it will show:

Time = 5:00:00 + 0:02:24

Time = 5:02:24 PM

Hence, the clock will show 5:02:24 at 5 PM.

Therefore, the correct answer is 5:02:24.

The logic followed in this series: Rotation of the grid along with shapes

Hence, the correct image is "Option 1".

The logic followed in this series: Rotation of box in clockwise direction while the number of circles decreasing and number of triangles increasing in each step.

Hence, the correct answer is "Option 1".

The logic followed in this series is:

​

Hence, the correct answer is "Option 4".

The correct answer is Chaniya choli (traditional skirt and blouse) with ornaments.

Key Points

• The Tippani dance is a vibrant folk dance originating from the Saurashtra region of Gujarat, traditionally performed by women from the Koli and Gola communities.
• The performers wear the iconic Chaniya choli, which consists of a long, flared skirt called the Chaniya (or Ghagra) and a short, fitted blouse known as the Choli.
• This ethnic ensemble is typically made of brightly colored cotton or silk, often featuring intricate embroidery, mirror work, and heavy borders to reflect the cultural heritage of Gujarat.
• Accompanying the dress, women wear traditional ornaments such as heavy silver necklaces, chunky bangles, waistbands (Kandora), and earrings, which provide a rhythmic sound and visual appeal during the dance.
• A colorful Odhni or dupatta is draped over the head or shoulders, tucked into the waist to allow free movement while beating the Tippani sticks against the ground.
• Hence, Chaniya choli (traditional skirt and blouse) with ornaments is the correct attire.

 Additional Information

• Tippani Tool and Origin:
• The dance is named after the Tippani, a wooden mallet-like tool used by construction workers in Chorwad and Veraval to level floors.
• It transitioned from a labor activity into a folk art where women beat the floor in a rhythmic pattern, often accompanied by instruments like the Zanj, Manjira, Tabla, and Dhol.
• Significance of Jewelry:
• The ornaments are not merely decorative; they signify the marital status and social standing of the women in rural Gujarati communities.
• In the context of the dance, the mirror work on the attire catches the light, creating a shimmering effect that complements the high-energy movements of the dancers.

The correct answer is Black.

Key Points

• The Deccan Plateau is characterized by its vast stretches of Black soil, which is also scientifically referred to as Regur soil.
• This soil type originates from the weathering and denudation of basaltic rocks formed by ancient volcanic activity and lava flows during the Cretaceous period.
• Black soil is globally renowned for its high clay content, which grants it an exceptional capacity for moisture retention, crucial for agriculture in rain-fed areas.
• It exhibits a unique self-ploughing property; during the dry season, it develops deep vertical cracks that facilitate the oxygenation of the soil and internal drainage.
• Chemically, it is rich in essential plant nutrients such as Calcium Carbonate, Magnesium, Potash, and Lime, although it is typically deficient in Phosphorous and Nitrogen.
• Geographically, it dominates the North-Western part of the plateau, covering significant portions of Maharashtra, Gujarat, Madhya Pradesh, and the Malwa Plateau.

 Additional Information

• Black Cotton Soil:
• It is primarily used for the cultivation of Cotton, earning it the specific nomenclature Black Cotton Soil.
• Apart from cotton, it supports crops like Sugarcane, Wheat, Linseed, and Sunflowers.
• Alluvial Soil:
• Formed by the deposition of silts by the Himalayan rivers. It is the most widespread soil in the Indo-Gangetic plains but less common in the deep Deccan interior.
• Red Soil:
• Develops on crystalline igneous rocks in areas of low rainfall. Its color is due to a wide diffusion of Iron in crystalline and metamorphic forms.
• Laterite Soil:
• Formed under conditions of high temperature and heavy rainfall with alternating wet and dry periods, leading to intense leaching of silica and lime.

The correct answer is Victim-centric and restorative justice.

Key Points

• The Bharatiya Nyaya Sanhita (BNS), 2023 was enacted to replace the Indian Penal Code (IPC) of 1860, marking a paradigm shift from a colonial-era retributive approach to a modern framework prioritizing justice over mere punishment.
• The legislation introduces community service as a specific form of punishment for minor offenses (such as defamation and public misconduct), which is a core component of restorative justice aimed at offender reform.
• It empowers victims by mandating that they are informed of the investigation progress within 90 days, ensuring their participation and right to information throughout the legal process.
• Specific provisions have been strengthened to protect women and children, including the introduction of life imprisonment or the death penalty for gang rape of minors, reflecting a victim-centric protection model.
• The BNS facilitates easier access to justice through the introduction of Zero FIR and e-FIR, allowing victims to report crimes irrespective of the police station's jurisdiction.

 Additional Information

• Colonial penal code:
• This refers to the Indian Penal Code (IPC), 1860, drafted by Lord Macaulay. It was primarily designed to safeguard British colonial interests and focused on maintaining public order through harsh punitive measures.
• Criminal Justice Reforms:
• The BNS is part of a tripartite legal overhaul alongside the Bharatiya Nagarik Suraksha Sanhita (BNSS) and the Bharatiya Sakshya Adhiniyam (BSA), which replace the CrPC and Indian Evidence Act.
• The new laws emphasize forensic science, making it mandatory for crimes involving punishment of seven years or more to ensure higher conviction rates and scientific accuracy in trials.
• Organized crime and terrorism have been clearly defined for the first time within the general penal law to address modern security challenges effectively.

The correct answer is Sawar.

Key Points

• The Mansabdari system was the administrative framework of the Mughal Empire, formalized by Emperor Akbar around 1571 to organize the nobility and the military.
• Under this system, every officer was assigned a Mansab (rank), which was divided into two distinct components: Zat and Sawar.
• The term Sawar referred to the specific number of cavalrymen or horsemen that a Mansabdar was mandated to maintain for imperial military service.
• The Sawar rank determined the military strength provided by the official and governed the allowance granted for the upkeep of horses and troopers.
• To ensure the quality of the Sawar contingent, the Mughals implemented the Dagh (branding of horses) and Chehra (descriptive rolls of soldiers) systems to prevent fraud and substitution.
• The Sawar rank could never exceed the Zat rank, and the ratio between the two determined the sub-class (first, second, or third) of the Mansabdar within their specific grade.

 Additional Information

• Zat
• This indicated the personal rank and status of the officer in the imperial hierarchy.
• It was used to calculate the personal salary of the Mansabdar.
• Jagir
• These were land revenue assignments granted to Mansabdars in lieu of cash salaries.
• The holders, known as Jagirdars, collected revenue from these lands to cover their personal pay and the costs of their Sawar contingents.
• Zamindar
• Refers to hereditary landed intermediaries who had the right to collect land revenue from peasants.
• While Zamindars provided local stability and collected taxes, they were distinct from Mansabdars, who were appointed officials of the Mughal state.

The correct answer is A. Jayathilak.

Key Points

• A. Jayathilak, a senior 1991-batch Indian Administrative Service (IAS) officer, has been designated as the 50^th Chief Secretary of Kerala.
• He is scheduled to assume the highest administrative office in the state on April 1, 2025, succeeding the incumbent official.
• He takes over the position from Sarada Muraleedharan, who served as the 49^th Chief Secretary and retired from service on March 31, 2025.
• Prior to this elevation, A. Jayathilak served as the Additional Chief Secretary for the Revenue and Disaster Management and Taxes departments.
• During his career, he has held several key positions, including Secretary of SC/ST Development, Agriculture, and Planning, and also served as the Chairman of the Cochin Port Trust.
• His appointment was finalized by the Kerala State Cabinet under the chairmanship of Chief Minister Pinarayi Vijayan.

 Additional Information

• Chief Secretary Role and Predecessor:
• The Chief Secretary is the administrative head of the state government, acting as the principal advisor to the Chief Minister and the Secretary to the State Cabinet.
• Sarada Muraleedharan, whom Jayathilak succeeds, was only the fifth woman to hold the post in Kerala’s history.
• Other Distinguished Entities:
• Sudarshan Venu: He is the Managing Director of TVS Motor Company and a prominent leader in the Indian automotive industry.
• S. Mahendra Dev: An eminent economist who served as the Director of the Indira Gandhi Institute of Development Research (IGIDR) and Chairman of the Commission for Agricultural Costs and Prices (CACP).
• Sailesh C. Mehta: He is the Chairman and Managing Director of Deepak Fertilisers and Petrochemicals Corporation Ltd.

The correct answer is Lieutenant General Pratik Sharma.

Key Points

• Lieutenant General Pratik Sharma has been appointed as the General Officer Commanding-in-Chief (GOC-in-C) of the Northern Army Command in May 2025, succeeding his predecessor in this high-stakes military role.
• The Northern Command is a Command-level formation of the Indian Army, which was originally formed in 1908, disbanded in 1947, and re-raised on June 17, 1972.
• Headquartered at Udhampur in the Union Territory of Jammu and Kashmir, the command is responsible for managing India's borders with both Pakistan and China in the northern theater.
• The officer in this position oversees critical operational zones, including the Line of Control (LoC) in Jammu and Kashmir and the Line of Actual Control (LAC) in Ladakh, ensuring territorial integrity and national security.
• The Northern Command plays a pivotal role in conducting counter-insurgency and counter-terrorism operations (such as Operation Rakshak) within the region, making it one of the most active operational commands globally.

 Additional Information

• Operational Commands of the Indian Army:
• Western Command: Headquartered at Chandimandir, it manages the borders along Punjab and parts of Rajasthan.
• Eastern Command: Based in Kolkata, it is responsible for the borders with China, Myanmar, and Bangladesh in the northeastern sector.
• Southern Command: Located in Pune, it covers the southern peninsula and the desert sectors of the western border.
• South Western Command: Headquartered in Jaipur, it focuses on the strategic sectors of Rajasthan and Haryana.
• Central Command: Based in Lucknow, it serves as a strategic reserve and oversees the central sector of the border with China.
• Army Training Command (ARTRAC): Located in Shimla, it is responsible for formulating training doctrines and standards.

The correct answer is 100^th Amendment act, 2015.

Key Points

• The 100^th Amendment Act, 2015 was enacted to give effect to the acquiring of certain territories by India and the transfer of certain other territories to Bangladesh.
• This constitutional amendment ratified the Land Boundary Agreement (LBA) of 1974 and its 2011 Protocol, which were designed to resolve the long-standing border disputes and the issue of enclaves (Chhitmahals).
• As a result of this exchange, India transferred 111 enclaves (covering approximately 17,160 acres) to Bangladesh, while Bangladesh transferred 51 enclaves (covering approximately 7,110 acres) to India.
• The act primarily concerned the demarcation of boundaries and the exchange of adverse possessions in the border states of Assam, West Bengal, Meghalaya, and Tripura.
• To implement these territorial changes, the Parliament amended the First Schedule of the Constitution of India, which lists the states and territories of the Union.

 Additional Information

• 91^st Amendment Act, 2003:
• Restricted the size of the Council of Ministers to 15 percent of the total strength of the Lok Sabha or the State Legislative Assembly.
• It also strengthened the Anti-Defection Law by deleting the provision regarding the protection from disqualification in case of a split by one-third of the members.
• 96^th Amendment Act, 2011:
• Substituted the name Odia for Oriya in the Eighth Schedule of the Constitution.
• This change ensured the official recognition of the correct phonetic pronunciation and spelling of the language.
• 97^th Amendment Act, 2011:
• Granted constitutional status and protection to Cooperative Societies.
• It introduced Part IXB and Article 43B (promotion of cooperative societies) and added the right to form cooperatives under Article 19.

The correct answer is Constitutional Amendment Bills.

Key Points

• Under Article 368 of the Indian Constitution, a Constitutional Amendment Bill can be initiated in either the Lok Sabha or the Rajya Sabha. It does not require the prior recommendation of the President for introduction.
• Both houses of Parliament exercise co-equal powers because such a bill must be passed in each House separately by a special majority. This requires a majority of the total membership of the house and a majority of not less than two-thirds of the members present and voting.
• The Constitution does not provide for a joint sitting under Article 108 in case of a deadlock between the two houses regarding an Amendment Bill. If the Rajya Sabha rejects the bill, the bill fails immediately, giving the Council of States an absolute veto equal to that of the House of the People.
• Upon being passed by both houses (and ratified by State Legislatures where necessary), the President must give assent to the bill. The 24^th Constitutional Amendment Act, 1971, made it mandatory for the President to sign the bill, ensuring parliamentary supremacy in the amendment process.

 Additional Information

• Money Bills:
• Governed by Article 110, these can only be introduced in the Lok Sabha. The Rajya Sabha has no power to reject or amend them and must return them within 14 days; otherwise, they are deemed passed.
• No-Confidence Motion:
• As per Article 75, the Council of Ministers is collectively responsible only to the Lok Sabha. Therefore, a No-Confidence Motion cannot be introduced or passed in the Rajya Sabha.
• Election of President:
• While elected members of both houses participate in the Electoral College under Article 54, the Rajya Sabha's specific legislative parity is most distinctly defined in the procedure for Constitutional Amendments where no joint sitting is possible.

The correct answer is Udhwa lake.

Key Points

• The Udhwa Lake Bird Sanctuary, situated in the Sahibganj district, is the only bird sanctuary in the state of Jharkhand.
• It consists of two main interconnected water bodies, namely Patauda Lake and Berhale Lake, spanning an area of about 5.65 square kilometers.
• This natural wetland serves as a crucial habitat for a diverse range of avian species, particularly migratory birds arriving via the Central Asian Flyway during winters.
• Due to its distinct ecological value and wetland characteristics, it has been proposed as the first potential Ramsar site from the state of Jharkhand to receive international recognition under the Ramsar Convention.

 Additional Information

• Khecheopalri wetland:
• Located in the West Sikkim district of Sikkim.
• It features a sacred lake surrounded by dense forests that holds deep religious significance for both Buddhists and Hindus.
• Sakkarakottai bird sanctuary:
• Located in the Ramanathapuram district of Tamil Nadu.
• It is a designated protected area that acts as an important staging and breeding ground for local and migratory waterbirds.
• Therthangal bird sanctuary:
• Also situated in the Ramanathapuram district of Tamil Nadu.
• It features a seasonal tank that supports large congregations of nesting bird species like the spot-billed pelican and Painted Stork.

The correct answer is SLV-3.

Key Points

• The Satellite Launch Vehicle-3 (SLV-3) was India's first indigenous experimental satellite launch vehicle, developed by the Indian Space Research Organisation (ISRO).
• It was a four-stage vehicle that used solid propellant in all its stages, reaching a height of approximately 22 meters.
• On July 18, 1980, the SLV-3 successfully deployed the Rohini satellite (RS-1) into a Low Earth Orbit (LEO).
• With this historic launch, India became the sixth nation in the world to possess the capability of launching satellites using its own indigenously developed technology.
• The project was led by Dr. A.P.J. Abdul Kalam, who served as the Project Director and played a pivotal role in the mission's success.
• While the initial flight in 1979 was a failure, the subsequent successful launches in the 1980s (1980 and 1983) paved the way for advanced rocket technology in India.

 Additional Information

• ASLV (Augmented Satellite Launch Vehicle)
• Designed to carry payloads up to 150 kg.
• Developmental flights began in 1987, but the first successful mission was achieved only in 1992.
• PSLV (Polar Satellite Launch Vehicle)
• Known as the Workhorse of ISRO, it is a third-generation launch vehicle.
• The first successful launch occurred in October 1994.
• It was the first Indian launch vehicle to be equipped with liquid stages.
• GSLV (Geosynchronous Satellite Launch Vehicle)
• A fourth-generation vehicle designed to place heavy satellites into Geosynchronous Transfer Orbit (GTO).
• Its maiden flight took place on April 18, 2001.
• It utilizes the Cryogenic Upper Stage (CUS) for high thrust at extreme temperatures.

The correct answer is IIT Guwahati.

Key Points

• Researchers at the Indian Institute of Technology (IIT) Guwahati developed a specialized water-repellent and conductive textile in February 2025, marking a significant advancement in material science.
• The textile is engineered to be superhydrophobic, meaning it possesses a water contact angle greater than 150 degrees, which prevents water from wetting the surface and allows droplets to roll off easily.
• By integrating conductive nanomaterials onto ordinary fabrics, the researchers created a material that maintains high electrical conductivity even while being exposed to moisture or humidity.
• The innovation is primarily designed for smart wearable electronics, allowing sensors and circuits embedded in clothing to remain functional during rain or heavy perspiration.
• This multi-functional textile can be used for human motion sensing, where it detects minute changes in electrical resistance during physical activities like joint movement or pulse tracking.

 Additional Information

• Smart Textiles and Wearables:
• Conductivity: Achieved through the application of materials like carbon nanotubes, graphene, or conductive polymers such as polypyrrole.
• EMI Shielding: These textiles can protect against Electromagnetic Interference, which is vital for aerospace and defense applications.
• Durability: One of the key challenges addressed by the IIT Guwahati team was ensuring the conductive coating remains stable after multiple wash cycles and mechanical stretching.
• Self-Cleaning Property: The superhydrophobic nature provides a Lotus Effect, where water droplets carry away dust particles, making the fabric self-cleaning.
• Energy Harvesting: Future iterations of such textiles may include triboelectric nanogenerators to harvest energy from body movements.

The correct answer is Diamond.

Key Points

• The Majhgawan mine is located in the Panna district of Madhya Pradesh and is internationally recognized as the only active mechanized diamond mine in Asia.
• The mine is owned and operated by the National Mineral Development Corporation (NMDC), a government-owned enterprise under the Ministry of Steel.
• Geologically, the diamonds at Majhgawan are hosted within a Kimberlite pipe, which is an igneous rock formation that originates from depths of over 150 kilometers in the Earth's mantle.
• This specific pipe is dated to approximately 1,100 million years ago, belonging to the Vindhyan Supergroup of rocks.
• The mine has a production capacity of roughly 84,000 carats per annum and contributes significantly to India’s total diamond production.
• The Panna diamond belt, where this mine is situated, extends over a length of about 240 kilometers and a width of 12 kilometers.

 Additional Information

• Lithium:
• Major reserves of Lithium were recently discovered in the Salal-Haimana area of Reasi district in Jammu & Kashmir.
• It is known as White Gold due to its high value and essential role in manufacturing rechargeable batteries for electric vehicles.
• Cobalt:
• In India, Cobalt is primarily found in Odisha (associated with nickel ores in Sukinda) and Jharkhand (Singhbhum district).
• It is a critical mineral used for making superalloys, catalysts, and lithium-ion battery cathodes.
• Silver:
• The largest production of Silver in India comes from Rajasthan, primarily from the Zawar mines and Rajpura-Dariba mines.
• It is usually extracted as a byproduct during the processing of Lead and Zinc concentrates from Galena and Sphalerite ores.

The correct answer is 1997.

Key Points

• The conceptualization of a Formula 1 race in India dates back to 1997, when a formal proposal was made to host the event in the city of Kolkata, West Bengal.
• During this period, there were discussions about constructing a street circuit to host the Indian Grand Prix, aiming to boost the country's profile in international motorsports.
• The 1997 initiative was driven by local promoters who sought to bring the FIA Formula One World Championship to India, but the plan faced significant logistical hurdles and a lack of government clearances at the time.
• Although the Kolkata project did not come to fruition, it serves as the earliest recorded milestone in the timeline of India's efforts to host a Grand Prix, eventually leading to interest from other cities like Bangalore and Hyderabad.
• This early attempt laid the groundwork for future negotiations between the Federation of Motor Sports Clubs of India (FMSCI) and Bernie Ecclestone, the then-chief of Formula 1.

 Additional Information

• Buddh International Circuit (BIC):
• The vision of an Indian Grand Prix was finally realized in 2011 at the Buddh International Circuit in Greater Noida, Uttar Pradesh.
• The circuit was designed by the world-renowned track architect Hermann Tilke and has a length of approximately 5.125 kilometers.
• Key Statistics of the Indian Grand Prix:
• The race was held for three consecutive years: 2011, 2012, and 2013.
• Sebastian Vettel, driving for Red Bull Racing, remains the only driver to have ever won the Indian Grand Prix, clinching victory in all three editions.
• Promoters and Drivers:
• The event was promoted by the Jaypee Group (JPSK Sports), which invested heavily in the Grade 1 racing facility.
• The rise of Indian drivers like Narain Karthikeyan (who debuted in 2005) and Karun Chandhok (who debuted in 2010) played a pivotal role in popularizing Formula 1 in India during this era.

The correct answer is South America.

Key Points

• MERCOSUR, which stands for Mercado Común del Sur (Southern Common Market), is a major regional integration process and trading bloc established to promote free trade and the fluid movement of goods, people, and currency across the continent of South America.
• The organization was officially established on March 26, 1991, following the signing of the Treaty of Asunción by the founding member nations.
• The primary founding members of the bloc are Argentina, Brazil, Paraguay, and Uruguay, all of which are located in the Southern Cone of South America.
• Its main objective is to foster a common market by eliminating customs duties between member states and establishing a common external tariff for trade with non-member nations.
• The bloc represents one of the world"s largest economic powers, characterized by significant agricultural exports, industrial manufacturing, and energy resources.

 Additional Information

• Member Status and Expansion:
• Venezuela joined as a full member in 2012 but has been suspended since December 2016 due to non-compliance with the bloc"s democratic clauses and trade regulations.
• Associate Members include other South American countries such as Chile, Colombia, Ecuador, Guyana, Peru, and Suriname, which enjoy preferential trade terms but lack full voting rights.
• Bolivia has been in the process of transitioning from an associate member to a full member status.
• Governance and Language:
• The administrative headquarters, known as the MERCOSUR Secretariat, is located in Montevideo, Uruguay.
• The official working languages are Spanish and Portuguese, reflecting the linguistic heritage of the Ibero-American nations.
• Regional Comparison:
• Unlike the European Union (Europe) or ASEAN (Asia), MERCOSUR specifically targets the socioeconomic integration of the South American region through the Protocol of Ouro Preto, which provided the bloc with its international legal personality.

The correct answer is Power tumbling.

Key Points

• Power tumbling, frequently called Tumbling, is a high-intensity gymnastics discipline that involves performing a series of explosive acrobatic maneuvers on a specialized sprung runway.
• The runway used in this sport is typically 25 meters long and provides a significant rebound effect, allowing gymnasts to achieve substantial height for complex mid-air rotations and twists.
• A standard competitive pass consists of eight consecutive elements, such as round-offs, flic-flacs (back handsprings), and saltos, which must be executed with continuous momentum and without hesitation.
• The sport is governed by the Federation Internationale de Gymnastique (FIG) and is a featured event in the Trampoline and Tumbling World Championships and the World Games.
• Judging is based on both the degree of difficulty (D-score) and the execution (E-score), emphasizing form, control, and the landing of the final skill within a designated landing zone.

 Additional Information

• Pen hold grip:
• This is a classic technique in Table Tennis where the player holds the paddle handle similarly to how one holds a writing pen.
• It is predominantly utilized by elite players in China, Japan, and South Korea, offering superior wrist mobility for forehand attacks.
• Side spin drive:
• A technical stroke used in racket sports like Table Tennis or Tennis to impart lateral rotation on the ball.
• This causes the ball to curve in the air and deviate upon bouncing, making it difficult for the opponent to control the return.
• Popping crease:
• An essential boundary line in Cricket marked at each end of the pitch, situated 4 feet in front of the bowling crease.
• It serves as the limit for the batsman's ground and is used by the Umpire to determine run-outs, stumpings, and front-foot no-balls.

The correct answer is Hampi.

Key Points

• The Vithalswami Temple, often referred to as the Vittala Temple, is an architectural masterpiece located in Hampi, Karnataka.
• The temple was primarily constructed during the 15^th century under the reign of King Devaraya II and underwent significant expansions during the rule of Krishnadevaraya (1509−1529 CE) of the Vijayanagara Empire.
• Dedicated to Lord Vittala, a manifestation of Lord Vishnu, the temple is renowned for its Dravidian architectural style and intricate carvings.
• One of its most famous features is the Stone Chariot, a majestic structure standing in the courtyard, which is now depicted on the reverse side of the Indian 50 rupee note.
• The temple complex is also celebrated for its 56 musical pillars, known as Saptaswara or SaReGaMa pillars, which emit musical notes when struck gently.

 Additional Information

• Hampi:
• Situated on the banks of the Tungabhadra River, it was the capital of the Vijayanagara Empire.
• It is recognized as a UNESCO World Heritage Site due to its vast collection of ruins and temples.
• Puri:
• Located in Odisha, it is famous for the Jagannath Temple and the Ratha Yatra festival.
• It is one of the four Char Dham pilgrimage sites in India.
• Gwalior:
• A historic city in Madhya Pradesh known for the Gwalior Fort and the Sas-Bahu Temple.
• It has been designated as a City of Music by UNESCO.
• Dispur:
• It is the capital of the state of Assam, situated within the Guwahati metropolitan area.

The correct answer is Kashmir.

Key Points

• Sufiana Kalam is the traditional classical music genre of the Kashmir Valley, representing a unique confluence of Central Asian, Persian, and Indian musical traditions.
• The word Muquam (derived from the Arabic/Persian Maqam) refers to the specialized melodic modes used in this style; there are traditionally 54 muquams, each corresponding to specific times of the day or particular seasons.
• This musical form is primarily devotional and mystical, used to recite the verses of prominent Sufi saints and poets such as Rumi, Hafiz, and Jami, as well as indigenous Kashmiri poets.
• The Santoor, a 100-stringed hammered dulcimer, serves as the lead accompanying instrument, providing the rhythmic and melodic framework essential to the Sufiana ensemble.
• The tradition flourished under the patronage of the Sultans of Kashmir, notably Zain-ul-Abidin (Budshah), who integrated musicians from Samarkand and Iran into his court during the 15^th century.

 Additional Information

• Kashmiri Musical Instruments:
• Saaz-e-Kashmir: A bowed string instrument specifically used in Sufiana Kalam to echo the vocal melodies.
• Kashmiri Setar: A long-necked lute with three or more strings, distinct from the Hindustani Sitar, used to maintain the drone and rhythm.
• Dukra: A pair of hand drums similar to the Tabla, used to provide the rhythmic cycles known as Taals.
• Other Regional Classical/Folk Styles:
• Kerala: Home to Sopana Sangeetham, a form of classical music sung at the holy steps of temples, and Carnatic music influences.
• West Bengal: Renowned for Baul Sangeet, a folk tradition of mystic minstrels, and Rabindra Sangeet.
• Telangana: Known for the Oggu Katha narrative tradition and various Deccani musical influences.

The correct answer is Jayaprakash Narayan.

Key Points

• Jayaprakash Narayan, revered as Loknayak (Leader of the People), was a preeminent Indian independence activist, social reformer, and political leader.
• He conceptualized the idea of Total Revolution (Sampoorna Kranti) in 1974, which aimed at a comprehensive transformation of the Indian society across seven spheres: political, social, economic, cultural, ideological, educational, and spiritual.
• The Total Revolution movement was primarily launched in Bihar as a peaceful agitation against corruption, high inflation, and the perceived authoritarianism of the central government led by Indira Gandhi.
• During the Quit India Movement of 1942, he played a legendary role in the underground resistance after his heroic escape from the Hazaribagh Central Jail, making him a symbol of socialist activism in India.
• He was posthumously awarded the Bharat Ratna, India's highest civilian honor, in 1999, in recognition of his lifelong service to the nation and the cause of democracy.

 Additional Information

• Morarji Desai:
• He served as the 4^th Prime Minister of India and led the first non-Congress government under the Janata Party in 1977.
• He is distinguished as the only Indian citizen to receive both the Bharat Ratna and Pakistan's highest civilian award, Nishan-e-Pakistan.
• Rajendra Prasad:
• The first President of India, he served from 1950 to 1962 and was the President of the Constituent Assembly.
• He is affectionately known as Desh Ratna and Ajatshatru for his humble nature and contribution to the freedom struggle.
• Lal Bahadur Shastri:
• The second Prime Minister of India, he is remembered for his leadership during the Indo-Pakistan War of 1965.
• He gave the iconic slogan Jai Jawan Jai Kisan to underscore the importance of soldiers and farmers in nation-building.

The correct answer is Janaagraha Centre for Citizenship and Democracy.

Key Points

• The Annual Survey of India's City-Systems (ASICS) is a flagship report published by the Janaagraha Centre for Citizenship and Democracy, a Bengaluru-based non-profit organization founded in 2001.
• The survey provides a detailed health check of India's urban governance by evaluating the 'city-systems' framework, which comprises the laws, policies, institutions, and processes that govern Indian cities.
• Unlike outcome-oriented rankings like the Swachh Survekshan or Ease of Living Index, ASICS evaluates the systemic reforms necessary to improve service delivery and urban infrastructure.
• The report assesses cities across four key pillars: Urban Planning and Design, Urban Capacities and Resources, Empowered and Legitimate Political Representation, and Transparency, Accountability, and Participation.
• ASICS serves as a diagnostic tool for policymakers and urban practitioners to identify legal and institutional gaps that hinder effective urban development in major state capitals and metropolitan areas.
• The survey often highlights critical issues such as the lack of financial autonomy for Urban Local Bodies (ULBs), limited powers of Mayors, and the shortage of skilled urban planners in Indian municipalities.

 Additional Information

• Janaagraha Centre for Citizenship and Democracy:
• It focuses on transforming the quality of life in Urban India through the City-Systems framework.
• Apart from ASICS, it works on initiatives like I Change My City and programs related to Municipal Finance and Civic Learning.
• NITI Aayog:
• The premier policy think tank of the Government of India, established on 1 January 2015.
• It publishes various indices such as the SDG India Index, School Education Quality Index, and State Health Index.
• Ministry of Social Justice and Empowerment:
• The nodal ministry for the welfare of Scheduled Castes, Backward Classes, Persons with Disabilities, and the Elderly.
• It implements acts like the Rights of Persons with Disabilities Act, 2016.

The correct answer is The Cayman Islands.

Key Points

• The Global Business Complexity Index (GBCI) is an annual comprehensive report published by the TMF Group, analyzing the administrative and regulatory environments of 79 jurisdictions that account for the majority of the world's Foreign Direct Investment (FDI) and GDP.
• In the 2024/2025 ranking cycle, the Cayman Islands is ranked at the 79^th position, identifying it as the least complex jurisdiction globally for business operations.
• The index measures complexity across three core areas: Accounting and Tax, HR and Payroll, and Global Entity Management (incorporation and compliance).
• The Cayman Islands maintains this ranking due to its tax-neutral status, lack of direct corporate taxes, and highly efficient regulatory framework designed to facilitate international financial services.
• The GBCI utilizes over 290 indicators to determine the ease or difficulty of operating in a specific country, focusing on the time and cost required to comply with local laws.

 Additional Information

• Global Complexity Trends:
• Countries like Greece, France, and Colombia are typically found at the top of the index, representing the highest complexity due to frequent legislative changes and intricate labor laws.
• The Netherlands is recognized for its digitalization and transparency, often ranking in the lower half of the index, signifying a relatively friendly business environment.
• Norway maintains low complexity through its advanced technological infrastructure and the Altinn portal, which streamlines reporting for businesses.
• Mauritius remains a preferred investment gateway for Africa, utilizing its Double Taxation Avoidance Agreements (DTAAs) and simple incorporation processes to attract global entities.
• The GBCI report highlights that geopolitical tensions and inflationary pressures are currently the primary drivers of regulatory shifts in most developed jurisdictions.

Shortcut Trick

Solve using BODMAS priority: Brackets first, then Multiplication, then Addition/Subtraction.

Calculate Bracket and Multiplication: (29 + 19) × 2 = 48 × 2 = 96

Group positive and negative values: (61 + 84 + 96) − (49 + 83)

Perform final calculation: 241 − 132 = 109

∴ The correct answer is 109.

Alternate Method

Given: 61 + 84 − 49 + (29 + 19) × 2 − 83

Formula Used: BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

⇒ 61 + 84 − 49 + (48) × 2 − 83

⇒ 61 + 84 − 49 + 96 − 83

⇒ (61 + 84 + 96) − 49 − 83

⇒ 241 − 49 − 83

⇒ 192 − 83

⇒ 109

∴ The correct answer is 109.

Additional Information

BODMAS Rule

The acronym stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction, defining the correct sequence of operations.

Priority of Brackets

Always solve the innermost brackets first in the sequence: round brackets ( ), then curly brackets { }, and finally square brackets [ ].

Grouping Method

For faster manual calculation, sum all positive terms and all negative terms separately before performing the final subtraction.

Shortcut Trick

Solve the expression directly using the BODMAS rule (Bracket, Division, Multiplication, Addition, Subtraction).

⇒ 71 + 27 − 34 + 18 + 13 + 21

⇒ (71 + 27 + 18 + 13 + 21) − 34

⇒ 150 − 34 = 116

∴ The correct answer is 116.

Alternate Method

Given: 71 + 27 − 34 + (18 × 1) + 39 ÷ 3 + 21

Formula Used: BODMAS Rule

⇒ 71 + 27 − 34 + 18 + 39 ÷ 3 + 21 (Solving Bracket: 18 × 1)

⇒ 71 + 27 − 34 + 18 + 13 + 21 (Solving Division: 39 ÷ 3)

⇒ 98 − 34 + 18 + 13 + 21 (Solving Addition from left to right)

⇒ 64 + 18 + 13 + 21 (Solving Subtraction)

⇒ 82 + 13 + 21

⇒ 95 + 21

⇒ 116

∴ The correct answer is 116.

Additional Information

BODMAS Rule

The BODMAS rule defines the order of operations: Brackets ((), {}, []), Orders (powers, roots), Division, Multiplication, Addition, and Subtraction.

Priority of Operations

Division and Multiplication hold the same priority level and should be solved from left to right as they appear. Similarly, Addition and Subtraction are solved from left to right.

Simplification Tip

To minimize errors in expressions with multiple additions and subtractions, group all positive terms together and all negative terms together before final calculation.

Shortcut Trick

8 men finish work in 12 days ⇒ 4 men finish work in 24 days.

12 women finish work in 18 days ⇒ 6 women finish work in 36 days.

Time taken by 4 men and 6 women = (24 × 36) ÷ (24 + 36) = 864 ÷ 60.

Total time taken = 14.4 days.

∴ The correct answer is 14.4 days.

Alternate Method

Given:

Total work capacity of 8 men in 12 days = Total work capacity of 12 women in 18 days.

⇒ 96 men = 216 women

⇒ 4 men = (216 ÷ 96) × 4 = 9 women

Total Group (4 men + 6 women) = 9 women + 6 women = 15 women.

⇒ Total Work = Women × Days = 12 × 18 = 216 units.

⇒ Days for 15 women = Total Work ÷ Number of women

⇒ Required Days = 216 ÷ 15 = 14.4 days.

∴ The correct answer is 14.4 days.

Additional Information

Work Equivalence Formula

For problems involving different groups, use M₁D₁H₁ ÷ W₁ = M₂D₂H₂ ÷ W₂ to find the relation between efficiencies.

Inverse Proportion of Men and Days

The number of people required to complete a work is inversely proportional to the time taken (M₁ × D₁ = M₂ × D₂).

Efficiency and Time

Efficiency = Total Work ÷ Total Time. If efficiency doubles, the time required to complete the same work becomes half.

Shortcut Trick

Separate the whole numbers and fractions: (3 + 33 + 333 + 3333 + 33333) + (1/3 + 1/15 + 1/35 + 1/63 + 1/99).

Sum of integers = 37035.

The fractional series follows the pattern 1/[n × (n + 2)]: (1/2) × [1/1 − 1/11] = 5/11.

Final result = 37035 + 5/11 = 37035 5/11.

∴ The correct answer is 37035 5/11.

Alternate Method

Given: 3 1/3 + 33 1/15 + 333 1/35 + 3333 1/63 + 33333 1/99

A mixed fraction a b/c is equivalent to a + b/c.

⇒ Total = (3 + 33 + 333 + 3333 + 33333) + (1/3 + 1/15 + 1/35 + 1/63 + 1/99)

⇒ Sum of whole numbers = 3 × (1 + 11 + 111 + 1111 + 11111) = 3 × 12345 = 37035

⇒ Sum of fractions (F) = 1/(1×3) + 1/(3×5) + 1/(5×7) + 1/(7×9) + 1/(9×11)

⇒ Using telescoping decomposition: 1/[n(n+d)] = (1/d) × [1/n − 1/(n+d)]

⇒ F = (1/2) × [(1/1 − 1/3) + (1/3 − 1/5) + (1/5 − 1/7) + (1/7 − 1/9) + (1/9 − 1/11)]

⇒ F = (1/2) × [1/1 − 1/11] = (1/2) × 10/11 = 5/11

⇒ Total = 37035 + 5/11 = 37035 5/11

∴ The correct answer is 37035 5/11.

Additional Information

Telescoping Series

The sum of a series where internal terms cancel out is found by: [1/Common Difference] × [1/First Term − 1/Last Term].

Mixed Fractions Addition

Always separate integers from fractions to simplify calculations in mixed fraction series.

Repeating Digit Sums

Sums like 3 + 33 + 333 + ... + 3(n times) can be calculated as [3 × (10ⁿ⁺¹ − 10 − 9n)] / 81 or simply by digit alignment.

Shortcut Trick

Apply the BODMAS rule to solve the expression efficiently.

First, calculate the product: 0.6 × 0.2 = 0.12.

Then, calculate the difference: 0.85 − 0.75 = 0.10.

Add the results: 0.12 + 0.10 = 0.22.

∴ The correct answer is 0.22.

Alternate Method

Given:

Expression: 0.6 × 0.2 + 0.85 − 0.75

Method:

Use the BODMAS rule (Multiplication → Addition → Subtraction).

Calculations:

⇒ (0.6 × 0.2) + 0.85 − 0.75

⇒ 0.12 + 0.85 − 0.75

⇒ 0.97 − 0.75

⇒ 0.22

∴ The correct answer is 0.22.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Decimal Multiplication

Multiply decimal numbers as whole numbers first, then place the decimal point based on the total number of decimal places in the original numbers.

Decimal Alignment

During addition or subtraction, always align the decimal points vertically to ensure correct place value calculation.

Shortcut Trick

The expression follows the algebraic identity: a³ − b³ − 3ab(a − b) = (a − b)³.

By comparing, let a = 50 and b = 20. Note that (a − b) = 50 − 20 = 30.

Substituting these values, the expression becomes (50 − 20)³ = 30³.

30³ = 30 × 30 × 30 = 27000.

∴ The correct answer is 27000.

Alternate Method

Given: 50³ − 20³ − 3 × 50 × 20 × 30

Method: Step-by-step arithmetic simplification.

⇒ 50³ = 50 × 50 × 50 = 125000

⇒ 20³ = 20 × 20 × 20 = 8000

⇒ 3 × 50 × 20 × 30 = 3 × 1000 × 30 = 90000

⇒ 125000 − 8000 − 90000

⇒ 117000 − 90000 = 27000

∴ The correct answer is 27000.

Additional Information

Algebraic Identity (a − b)³

The cube of a difference is expanded as (a − b)³ = a³ − b³ − 3ab(a − b).

Algebraic Identity (a + b)³

The cube of a sum is expanded as (a + b)³ = a³ + b³ + 3ab(a + b).

Difference of Two Cubes

The factorization of the difference of two cubes is a³ − b³ = (a − b)(a² + ab + b²).

Shortcut Trick

Perimeter of a square = 4 × Side = 28 cm

Side = 28 ÷ 4 = 7 cm

Diagonal = Side × √2 = 7√2 cm

∴ The correct answer is 7√2 cm.

Alternate Method

Given: Perimeter of the square = 28 cm

Formula Used:

1. Perimeter (P) = 4 × a (where 'a' is the side)
2. Diagonal (d) = a√2

Calculations:

⇒ 4 × Side = 28 cm

⇒ Side = 28 ÷ 4

⇒ Side = 7 cm

⇒ Diagonal = Side × √2

⇒ Diagonal = 7 × √2 = 7√2 cm

∴ The correct answer is 7√2 cm.

Additional Information

Area of a Square

The Area can be calculated as Side² or (Diagonal²) ÷ 2.

Relationship between Side and Diagonal

In any square, the diagonal is always √2 times the length of its side (d = a√2).

Pythagoras Theorem in Square

Since all angles of a square are 90°, the diagonal forms two right-angled triangles where Side² + Side² = Diagonal².

Shortcut Trick

Side of a square = Perimeter ÷ 4

Diagonal of a square = Side × √2

Side = 24 ÷ 4 = 6 cm

Diagonal = 6 × √2 = 6√2 cm

∴ The correct answer is 6√2 cm.

Alternate Method

Given:

Perimeter of the square = 24 cm

Formula Used:

Perimeter = 4 × side (a)

Diagonal (d) = a√2 (derived from Pythagoras Theorem: d² = a² + a²)

Calculations:

⇒ 4 × a = 24

⇒ a = 24 ÷ 4

⇒ a = 6 cm

⇒ Diagonal (d) = a × √2

⇒ Diagonal = 6 × √2

⇒ Diagonal = 6√2 cm

∴ The correct answer is 6√2 cm.

Additional Information

Area of a Square

The area can be calculated using the side as a² or using the diagonal as (d² ÷ 2).

Properties of a Square

All sides are equal, all angles are 90°, and diagonals are equal and bisect each other at 90°.

Side to Diagonal Ratio

In any square, the ratio of the side to the diagonal is always 1 : √2.

Shortcut Trick

The sum of the first n odd natural numbers is always n².

Number of terms (n) = (Last Term + 1) ÷ 2

n = (295 + 1) ÷ 2 = 148

Sum = 148² = 21904

∴ The correct answer is 21904.

Alternate Method

Given:

The series is an Arithmetic Progression (AP): 1, 3, 5, 7, ..., 295.

First term (a) = 1

Common difference (d) = 3 − 1 = 2

Last term (l) = 295

Formula Used:

n-th term: l = a + (n − 1)d

Sum of n terms: S_n = (n ÷ 2) × (a + l)

Calculations:

⇒ 295 = 1 + (n − 1) × 2

⇒ 295 − 1 = (n − 1) × 2

⇒ 294 = (n − 1) × 2

⇒ n − 1 = 147

⇒ n = 148

⇒ S₁₄₈ = (148 ÷ 2) × (1 + 295)

⇒ S₁₄₈ = 74 × 296

⇒ S₁₄₈ = 21904

∴ The correct answer is 21904.

Additional Information

Sum of first n Natural Numbers

The sum of first n natural numbers (1 + 2 + 3 + ... + n) is given by the formula: n(n + 1) ÷ 2.

Sum of first n Even Numbers

The sum of first n even numbers (2 + 4 + 6 + ... + 2n) is calculated using the formula: n(n + 1).

Sum of Squares of first n Natural Numbers

The sum of squares (1² + 2² + ... + n²) is given by: n(n + 1)(2n + 1) ÷ 6.

Shortcut Trick

New age = New Average + (Initial Count × Average Increase)

New Average = 45 + 2 = 47 years

Age = 47 + (14 × 2) = 47 + 28 = 75 years

∴ The correct answer is 75 years.

Alternate Method

Given:

Number of teachers = 14

Initial average = 45 years

Average increase = 2 years

Formula Used:

Sum of values = Average × Number of observations

Calculations:

⇒ Total age of 14 teachers = 14 × 45 = 630 years

⇒ Total teachers after inclusion = 14 + 1 = 15

⇒ New average age = 45 + 2 = 47 years

⇒ Total age of 15 teachers = 15 × 47 = 705 years

⇒ Age of new teacher = 705 − 630 = 75 years

∴ The correct answer is 75 years.

Additional Information

Net Deviation Method

When a new person joins, the net deviation from the old average must be distributed across all members. New Person = Old Average + (Total Members × Change in Average).

Including vs. Excluding

If a member is included and the average increases, their value is greater than the average. If a member is excluded and the average increases, their value was less than the average.

Weighted Average

Combined Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂), where n is the count and A is the average of respective groups.

Shortcut Trick

Initial Average of 15 boys = 55

After removing 2 boys, the average reduces to 54 (reduction of 1 per boy)

Sum of removed items (H + L) = (2 × Old Average) + (New Count × Reduction)

Sum of H + L = (2 × 55) + (13 × 1) = 110 + 13 = 123

Average of highest and lowest marks = 123 ÷ 2 = 61.5

∴ The correct answer is 61.5.

Alternate Method

Given:

Total number of boys = 15

Initial average marks = 55

Number of boys after removing highest and lowest = 13

New average marks = 55 − 1 = 54

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Total sum of marks for 15 boys = 15 × 55 = 825

⇒ Total sum of marks for 13 boys = 13 × 54 = 702

⇒ Sum of marks of (Highest + Lowest) = 825 − 702 = 123

⇒ Average of (Highest + Lowest) = 123 ÷ 2 = 61.5

∴ The correct answer is 61.5.

Additional Information

Average Concept

The Arithmetic Mean or average is the ratio of the sum of all observations to the total number of observations (Sum ÷ n).

Exclusion Principle

When values are removed from a group, the sum of removed values is equal to (Initial Total Sum) − (New Total Sum).

Impact on Average

If the average reduces after removing items, it means the average of the removed items was higher than the original average of the group.

Shortcut Trick

Total ratio parts for the sum = 3 + 5 = 8 parts.

Since the Highest Common Factor (HCF) represents the value of 1 unit in the ratio.

Sum of numbers = 8 × 18 = 144.

∴ The correct answer is 144.

Alternate Method

Given:

Ratio of two numbers = 3 : 5

Highest Common Factor (HCF) = 18

Formula Used:

If the ratio of two numbers is a : b and their HCF is h, then the numbers are (a × h) and (b × h).

Calculations:

⇒ Let the two numbers be 3x and 5x.

⇒ The HCF of 3x and 5x is x (since 3 and 5 are coprime).

⇒ Given x = 18.

⇒ First number = 3 × 18 = 54.

⇒ Second number = 5 × 18 = 90.

⇒ Sum of numbers = 54 + 90 = 144.

∴ The correct answer is 144.

Additional Information

Relationship between HCF and LCM

For any two numbers A and B, the product of the numbers is equal to the product of their HCF and LCM: A × B = HCF × LCM.

LCM from Ratio and HCF

If the ratio of two numbers is a : b and their HCF is h, then their Least Common Multiple (LCM) = a × b × h.

HCF of Coprime Numbers

If two numbers have no common factor other than 1, they are called coprime and their HCF is always 1.

Shortcut Trick

Find the Least Common Multiple (LCM) of the given intervals: 5, 10, 15, 20, 25, and 30 seconds.

LCM (5, 10, 15, 20, 25, 30) = 300 seconds = 5 minutes.

Number of times the bells ring together = (Total Time ÷ LCM) + 1.

Required times = (20 ÷ 5) + 1 = 4 + 1 = 5 times.

∴ The correct answer is 5 times.

Alternate Method

Given:

Intervals of six bells = 5, 10, 15, 20, 25, and 30 seconds.

Total time duration = 20 minutes.

Formula Used:

Common interval = LCM of individual intervals.

Number of rings = (Total duration ÷ Common interval) + 1 (to include the first ring).

Calculations:

⇒ Prime factorization of intervals:

5 = 5

10 = 2 × 5

15 = 3 × 5

20 = 2² × 5

25 = 5²

30 = 2 × 3 × 5

⇒ LCM = 2² × 3 × 5² = 4 × 3 × 25 = 300 seconds.

⇒ Common interval in minutes = 300 ÷ 60 = 5 minutes.

⇒ Total rings = (Total Duration ÷ Common Interval) + 1

⇒ Total rings = (20 ÷ 5) + 1 = 4 + 1 = 5 times.

∴ The correct answer is 5 times.

Additional Information

Least Common Multiple (LCM)

The smallest number that is a multiple of two or more numbers. In coincidence problems (bells, traffic lights), the LCM determines the next time all events occur simultaneously.

Commencement Rule

When the problem states "including the first ring at commencement" or "ringing together at the start", always add 1 to the division result: (Total Time ÷ Interval) + 1.

Unit Consistency

Before dividing, ensure the total time and the common interval are in the same unit (e.g., both in seconds or both in minutes).

Shortcut Trick

Ratio of Profit to Selling Price = 3 : 8.

Let Profit = 3 units and Selling Price = 8 units.

Cost Price = 8 − 3 = 5 units.

Profit Percentage = (3 ÷ 5) × 100 = 60%.

∴ The correct answer is 60%.

Alternate Method

Given:

Ratio of Profit (P) to Selling Price (SP) = 3 : 8

Formula Used:

1. Cost Price (CP) = Selling Price − Profit

2. Profit Percentage = (Profit ÷ Cost Price) × 100

Calculations:

⇒ Let Profit = 3x and Selling Price = 8x

⇒ Cost Price (CP) = 8x − 3x

⇒ Cost Price (CP) = 5x

⇒ Profit Percentage = (3x ÷ 5x) × 100

⇒ Profit Percentage = 0.6 × 100

⇒ Profit Percentage = 60%

∴ The correct answer is 60%.

Additional Information

Loss Percentage

Loss percentage is always calculated on the Cost Price unless specified otherwise. Formula: Loss % = (Loss ÷ CP) × 100.

Selling Price Calculation

When profit percentage is given: Selling Price = CP × (100 + Profit%) ÷ 100.

Marked Price and Discount

Discount is always offered on the Marked Price (MP). SP = MP − Discount.

Relation between CP and MP

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This is a key ratio for solving Markup problems.

Shortcut Trick

Effective Remaining Percentage = (100 − 30)% × (100 − 60)%

Remaining = 70% × 40% = 28% of the Initial Money.

Given that 28% = ₹2100.

100% = (2100 ÷ 28) × 100 = 75 × 100 = ₹7500.

∴ The correct answer is ₹7500.

Alternate Method

Given:

Money spent = 30%

Bank deposit = 60% of the remaining money

Final remaining amount = ₹2100

Calculations:

⇒ Let the initial money be ₹X.

⇒ After spending 30%, remaining money = X − 30% of X = 0.70X.

⇒ Bank deposit = 60% of 0.70X = 0.42X.

⇒ Final remaining money = 0.70X − 0.42X = 0.28X.

⇒ According to the question: 0.28X = 2100.

⇒ X = 2100 ÷ 0.28.

⇒ X = 210000 ÷ 28.

⇒ X = 7500.

∴ The correct answer is ₹7500.

Additional Information

Successive Percentage Change

When a value changes by a% and then the remaining value changes by b%, the net remaining value is (100 − a)% × (100 − b)% of the initial amount.

Percentage to Fraction Conversion

Calculations are faster using fractions: 30% = 3/10 (Remaining = 7/10) and 60% = 3/5 (Remaining = 2/5). Net remaining = 7/10 × 2/5 = 7/25.

Concept of Remaining

Always identify the base for each percentage calculation. If the problem states percent of remaining, the previous leftover value becomes the new 100%.

Shortcut Trick

If the Cost Price (CP) of 15 articles equals the Selling Price (SP) of 12 articles:

15 × CP = 12 × SP ⇒ CP/SP = 12/15 = 4/5.

Let CP = 4 units and SP = 5 units. Then Profit = 5 − 4 = 1 unit.

Required Ratio (Profit : SP) = 1 : 5.

∴ The correct answer is 1 : 5.

Alternate Method

Given: CP of 15 articles = ₹197; SP of 12 articles = ₹197.

Formula: Profit = Selling Price (SP) − Cost Price (CP).

⇒ CP of 1 article = ₹197/15

⇒ SP of 1 article = ₹197/12

⇒ Profit per article = (197/12) − (197/15)

⇒ Profit = 197 × (5 − 4) / 60 = ₹197/60

⇒ Ratio = (Profit of 1 article) : (SP of 1 article)

⇒ Ratio = (197/60) : (197/12)

⇒ Ratio = (1/60) × 12 = 12/60 = 1/5

∴ The correct answer is 1 : 5.

Additional Information

Profit Percentage Formula

Profit% is calculated on the Cost Price: Profit% = (Profit ÷ CP) × 100.

Inverse Relation of Quantity and Price

When the total value is constant, the ratio of Unit Prices is the inverse of the ratio of Quantities.

Ratio and SP

Profit margin on sales is the ratio of Profit to Selling Price, often used in retail accounting.

Shortcut Trick

Total Work = LCM (10, 20, 40) = 40 units.

Efficiency: A = 4, B = 2, C = 1 (Total = 7 units/day).

Work done by A, B, and C in 4 days = 7 × 4 = 28 units.

Remaining Work = 40 − 28 = 12 units.

Time for C = 12 ÷ 1 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Time taken by A = 10 days

Time taken by B = 20 days

Time taken by C = 40 days

Work duration of A and B = 4 days

Formula Used:

Efficiency = Total Work ÷ Time

Remaining Work = Total Work − Work Completed

Calculations:

⇒ Total efficiency of A, B, and C = 4 + 2 + 1 = 7 units/day.

⇒ Work completed in first 4 days = 7 × 4 = 28 units.

⇒ Remaining work to be done by C = 40 − 28 = 12 units.

⇒ Efficiency of C = 1 unit/day.

⇒ Days required by C = 12 ÷ 1 = 12 days.

∴ The correct answer is 12 days.

Additional Information

Pipes & Cisterns

Similar to time and work, but efficiency can be negative for outlet pipes (leakage). Total capacity acts as total work.

Work & Wages

Wages are distributed in the ratio of the actual work done by each individual, which is equal to the ratio of their efficiencies if they work for the same duration.

Alternate Day Work

In problems where workers work on alternate days, find the work done in one cycle (e.g., 2 or 3 days) and then calculate total time based on the cycle completion.

Shortcut Trick

When two objects move towards each other, their relative speed is the sum of their individual speeds.

Relative Speed = 55 + 35 = 90 km/hr

Time taken to meet = Total Distance ÷ Relative Speed

Time = 540 ÷ 90 = 6 hr

∴ The correct answer is 6 hr.

Alternate Method

Given:

Distance (D) = 540 km

Speed of R (S_R) = 55 km/hr

Speed of P (S_P) = 35 km/hr

Formula Used:

Time = Distance ÷ (S₁ + S₂) [When moving in opposite directions]

Calculations:

⇒ Relative Speed = S_R + S_P

⇒ Relative Speed = 55 + 35 = 90 km/hr

⇒ Time = Distance ÷ Relative Speed

⇒ Time = 540 ÷ 90

⇒ Time = 6 hr

∴ The correct answer is 6 hr.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds (S₁ − S₂).

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Time and Distance Relation

Distance = Speed × Time. If distance is constant, time is inversely proportional to speed.

Shortcut Trick

Total ratio parts = 14 + 11 = 25 units.

Given total weight of alloy = 275 kg.

25 units = 275 kg ⇒ 1 unit = 11 kg.

Amount of A = 14 units = 14 × 11 = 154 kg.

∴ The correct answer is 154 kg.

Alternate Method

Given:

Ratio of A : B = 14 : 11

Total weight of the alloy = 275 kg

Formula:

Amount of A = (Ratio part of A ÷ Total ratio parts) × Total Weight

Calculations:

⇒ Total parts = 14 + 11 = 25

⇒ Amount of A = (14 ÷ 25) × 275

⇒ Amount of A = 14 × (275 ÷ 25)

⇒ Amount of A = 14 × 11

⇒ Amount of A = 154 kg

∴ The correct answer is 154 kg.

Additional Information

Ratio and Proportion

If a quantity Z is divided in the ratio a : b, then the parts are [a / (a + b)] × Z and [b / (a + b)] × Z.

Percentage of Component

The percentage of a component in an alloy is calculated as: (Component Ratio ÷ Sum of Ratios) × 100.

Compounded Ratio

The compounded ratio of two ratios (a : b) and (c : d) is (ac : bd).

Shortcut Trick

Assume Income of P = 24 units → Income of Q = 54 units (Ratio 4 : 9).

Savings of P = 24 ÷ 6 = 4 units; Expenditure of P = 24 − 4 = 20 units.

Since Expenditure ratio is 3 : 5, Expenditure of Q = 20 × (5/3) = 100/3 units.

Savings of Q = Income − Expenditure = 54 − 100/3 = 62/3 units.

Ratio of Savings (P : Q) = 4 : (62/3) = 12 : 62 = 6 : 31.

∴ The correct answer is 6 : 31.

Alternate Method

Given:

Ratio of Incomes (P : Q) = 4 : 9

Ratio of Expenditures (P : Q) = 3 : 5

Savings of P = (1/6) × Income of P

Formula Used:

Savings = Income − Expenditure

Calculations:

⇒ Let Income of P = 4x and Income of Q = 9x.

⇒ Let Expenditure of P = 3y and Expenditure of Q = 5y.

⇒ Savings of P = 4x − 3y

⇒ Given 4x − 3y = (1/6) × 4x

⇒ 4x − 3y = 2x/3

⇒ 3y = 4x − 2x/3 = 10x/3 ⇒ y = 10x/9

⇒ Savings of Q = 9x − 5y = 9x − 5 × (10x/9)

⇒ Savings of Q = (81x − 50x) / 9 = 31x/9

⇒ Savings of P = 4x − 3(10x/9) = 4x − 10x/3 = 2x/3

⇒ Ratio of Savings (P : Q) = (2x/3) : (31x/9) = 6 : 31.

∴ The correct answer is 6 : 31.

Additional Information

Income, Expenditure and Savings Relationship

The fundamental equation for financial aptitude is Income = Expenditure + Savings. Any one component can be found if the other two are known or given in ratio form.

Ratio Scaling

When two different ratios are given (like Income and Expenditure), they cannot be compared directly unless a common variable or a specific condition (like Savings of P) relates them.

Fractional Savings

If savings is a fraction 'k' of income, then Expenditure = (1 − k) × Income. This helps in directly establishing the relationship between the two ratios.

The correct answer is: Option (1) i.e. Being watched or examined closely.

Key Points

• The idiom 'under close scrutiny' refers to a situation where someone or something is being subjected to very thorough, critical, and detailed observation or inspection. (बारीकी से जांच के अधीन)
• Example: The government's new policy has been under close scrutiny by the public and the media.
• 'Being watched or examined closely' means the act of monitoring or investigating something with extreme care to ensure accuracy or to find faults. (बारीकी से देखा या परखा जाना)
• Example: Every part of the engine is being watched or examined closely for signs of wear and tear.
• Hence, we can infer that the correct meaning of the idiom 'under close scrutiny' is 'being watched or examined closely'.

Therefore, the correct answer is- Being watched or examined closely.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Not being watched or examined closely (बारीकी से नहीं देखा या जांचा जाना): This implies a lack of supervision or a casual approach where details might be missed.
• Example: When the students are not being watched or examined closely, they tend to get distracted.
• Go unnoticed intentionally by the authority (अधिकारी द्वारा जानबूझकर अनदेखा किया जाना): This describes a situation where an official or person in charge deliberately ignores a mistake or action.
• Example: The building violation was allowed to go unnoticed intentionally by the authority due to political pressure.
• Being taught carefully (सावधानी से सिखाया जाना): This refers to receiving education or training with great attention to detail and patience.
• Example: The young pianist is being taught carefully by a world-renowned instructor.

The correct answer is: quick.

Key Points

• The word 'rapid' means happening in a short time or at a great speed; it describes a fast pace of movement or change. (तीव्र)
• Example: The country is experiencing rapid economic growth due to new industrial policies.
• 'Quick' refers to moving fast or doing something in a short amount of time; it is the closest synonym to rapid. (तेज़)
• Example: He gave a quick nod of approval before leaving the room.
• Hence, we can infer that the closest synonym of 'rapid' is 'quick'.

Therefore, the correct answer is- quick.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Slow (धीमा): Moving, operating, or happening at a low speed; not quick or fast.
• Example: The slow pace of the lecture made it difficult for the students to stay focused.
• Late (देर): Doing something or taking place after the expected, proper, or usual time.
• Example: I apologized for being late to the dinner party.
• Weak (कमजोर): Lacking the power to perform physically demanding tasks; having little physical strength or energy.
• Example: She felt weak and dizzy after skipping her breakfast.

The correct answer is Option(4) i.e. Rigourous.

Key Points

• The word 'Rigourous' is a misspelt word; the correct spelling of the adjective is 'Rigorous', which refers to something that is extremely thorough, exhaustive, or strictly applied. (कठोर)
• Example: The results were questioned because the researcher used a rigourous (misspelt) approach that lacked accuracy.
• 'Rigorous' refers to the quality of being extremely thorough and careful, often used to describe analysis, training, or standards. (सख्त)
• Example: The military training was incredibly rigorous, testing the recruits both physically and mentally.
• Hence, we can infer that the misspelt word among the given options is 'Rigourous'.

Therefore, the correct answer is- Rigourous.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Rhapsodic (उत्साही): Characterized by an intense or extravagant expression of enthusiasm or ecstasy.
• Example: He gave a rhapsodic account of his travels through the Italian countryside.
• Rapacious (लालची): Having or showing a strong or excessive desire to acquire money or possess things; aggressively greedy.
• Example: The rapacious speculators were blamed for the sudden rise in property prices.
• Resourceful (साधन-संपन्न): Having the ability to find quick and clever ways to overcome difficulties and solve problems.
• Example: A resourceful manager can find ways to keep a project on track even with a limited budget.

The correct answer is Forbid.

Key Points

• The word 'permit' means to give authorization or consent to someone to do something; it implies allowing an action to take place or making it possible. (अनुमति देना)
• Example: The security guards will not permit anyone to enter the building without a valid ID card.
• 'Forbid' means to refuse to allow something or to prohibit an action, making it the direct opposite of 'permit'. (मना करना)
• Example: The doctor had to forbid the patient from eating sugary foods due to health concerns.
• Hence, we can infer that the most appropriate antonym of 'permit' is 'forbid'.

Therefore, the correct answer is- Forbid.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Allow (अनुमति देना): To let someone do something or to not prevent something from happening.
• Example: Many parents do not allow their children to stay out late at night.
• Authorize (अधिकृत करना): To give official permission for something or to grant someone the authority to perform a task.
• Example: The Director is the only person who can authorize such a large expenditure.
• Approve (मंजूरी देना): To officially agree to or accept a proposal, plan, or request as satisfactory.
• Example: The committee is expected to approve the new budget by the end of the week.

The correct answer is: Calm.

Key Points

• The word 'Nervous' refers to a state of being anxious, worried, or easily agitated, especially regarding a future event or a stressful situation. (घबराया हुआ)
• Example: She felt extremely nervous as she waited for the results of her audition.
• 'Calm' refers to a state of being peaceful, composed, and free from agitation or strong emotions like anxiety or anger; it is the direct opposite of being nervous. (शांत)
• Example: The pilot stayed calm and managed to land the plane safely during the storm.
• Hence, we can infer that the antonym of 'Nervous' is 'Calm'.

Therefore, the correct answer is: Calm.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Anxious (चिंतित): Experiencing worry, unease, or nervousness about something with an uncertain outcome.
• Example: The students were anxious to see their final grades.
• Uneasy (बेचैन/असहज): Feeling uncomfortable, troubled, or restless due to a sense of impending danger or trouble.
• Example: He had an uneasy feeling that he had forgotten something important.
• Tense (तनावपूर्ण): A state where one is unable to relax because of nervousness or mental pressure.
• Example: The atmosphere in the room was tense as they waited for the verdict.

The correct answer is: Precursor.

Key Points

• The phrase 'A thing that comes before another thing of the same kind' describes an object or person that precedes another in time or development. (एक ही प्रकार की दूसरी चीज़ से पहले आने वाली चीज़)
• Example: The rotary dial phone was a precursor to the modern smartphone.
• 'Precursor' refers to something that happened or existed before another thing and had an influence on it or was a sign of what was to come. (पूर्वगामी)
• Example: Biological research on cells was a precursor to the development of modern vaccines.
• Hence, we can infer that the most suitable one-word substitution for the given phrase is 'precursor'.

Therefore, the correct answer is: Precursor.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Adage (कहावत): A traditional saying expressing a common experience or observation; a proverb.
• Example: My grandfather always used the adage, 'Waste not, want not' when we left food on our plates.
• Umbrage (अपमान का बोध/रोष): Feeling of being offended or resentful.
• Example: The politician took umbrage at the journalist's questioning of his integrity.
• Proximity (निकटता): The state of being near in space or time.
• Example: The proximity of the nuclear plant to the city raised safety concerns among the residents.

The correct answer is 'for'.

 

Key Points

• The preposition 'for' is used to indicate a period of time or duration.
• In the given sentence, 'two hr' (two hours) represents a specific length of time that the action of waiting lasted.
• The sentence is in the past perfect continuous tense ('had been waiting'), which typically uses 'for' to show how long an action had been continuing up to a point in the past.
• Option 1, 2, and 3 do not fit the grammatical requirement for expressing a duration of time in this context.

Therefore, the correct answer is Option 4.

 

Complete Sentence: 'Rishita said that she had been waiting at the gate for two hr.'

 

Additional Information

• Since: This is used to refer to a specific starting point in time (e.g., since 10 AM, since Monday).
• By: This is used to indicate a limit or deadline by which an action must be completed (e.g., by tomorrow).
• From: This is often used to show the beginning of a range of time, often paired with 'to' or 'until' (e.g., from morning to evening).

The correct answer is The underperforming employees will be fired by the manager..

Key Points

• The given sentence is in the Active Voice and follows the structure of the Simple Future Tense: Subject + will + V1 (base verb) + Object.
• In this sentence, The manager is the Subject, will fire is the Verb, and the underperforming employees is the Object.
• To convert a Simple Future Tense sentence into Passive Voice, the structure used is: New Subject (Object of active) + will + be + V3 (Past Participle) + by + New Agent (Subject of active).
• Following this rule, the object the underperforming employees moves to the subject position, and the verb will fire changes to will be fired.
• The original subject the manager is added at the end, preceded by the preposition by, resulting in the correct passive construction.

 Additional Information

• Understanding why other options are incorrect based on Tense and Modality:
• The underperforming employees must be fired by the manager: This uses the modal verb must, which changes the degree of necessity and does not reflect the original Simple Future intent of will.
• The underperforming employees will fire the manager: This sentence remains in the Active Voice but reverses the Subject and Object, fundamentally altering the meaning of the original statement.
• The underperforming employees are fired by the manager: This structure represents the Simple Present Tense in passive voice (is/am/are + V3), failing to maintain the future timeframe established by will.
• In English grammar, the Future Passive is essential for formal reporting where the action or the receiver of the action is more significant than the performer.

The correct answer is A hidden cave was discovered by the explorer behind the waterfall..

Key Points

• The original sentence 'The explorer discovered a hidden cave behind the waterfall' is in the Active Voice and follows the Subject + Verb (V2) + Object structure.
• The verb discovered is in the Simple Past Tense, which indicates an action completed at a specific time in the past.
• To convert a sentence from Active Voice to Passive Voice in the Simple Past Tense, the rule is: New Subject (Original Object) + was/were + Past Participle (V3) + by + New Object (Original Subject).
• In this sentence, the Object is a hidden cave. Since this is a Singular Noun, it must be paired with the singular auxiliary verb was to maintain Subject-Verb Agreement.
• The Past Participle form of the verb 'discover' is discovered.
• The prepositional phrase behind the waterfall remains as an adverbial modifier, and the agent the explorer is introduced using the preposition by.

 Additional Information

• Simple Present Passive:
• This uses is/am/are + V3. It is used for facts or regular actions (e.g., 'is discovered'), which does not match the Simple Past tense of the original verb.
• Present Perfect Passive:
• This uses has/have + been + V3. It represents an action that happened at an indefinite time (e.g., 'has been discovered'), whereas the original sentence used the definite Simple Past.
• Subject-Verb Agreement Errors:
• Using were with a singular subject like a hidden cave is grammatically incorrect, as were is reserved for plural subjects or the second person.

The correct answer is The students read the books every evening..

Key Points

• The given sentence is in the Passive Voice and follows the structure of the Simple Present Tense: Object + is/am/are + V3 (Past Participle) + by + Subject.
• To convert this into the Active Voice, the agent of the action (the students) must be moved to the beginning of the sentence to act as the subject.
• The auxiliary verb 'are' is removed, and the past participle 'read' is changed to its base form (V1) to maintain the Simple Present Tense.
• Since The students is a plural subject, the verb read remains in its base form without adding an 's' or 'es' (subject-verb agreement).
• The recipient of the action, The books, which was the subject in the passive form, is moved to the object position in the active form.
• The phrase every evening is an adverbial of frequency that indicates a habitual action, confirming that the tense must remain in the Present Indefinite/Simple Present.

 Additional Information

• Understanding why other options are incorrect based on Tense consistency:
• Present Perfect Tense: The option containing have read is incorrect because it changes the tense to indicate a completed action, which does not match the original Simple Present passive.
• Present Continuous Tense: The option are reading is incorrect because it describes an action currently in progress rather than a general habit or fact.
• Simple Future Tense: The option will read is incorrect as it shifts the timeframe to the future, violating the rule that the tense must remain the same during voice conversion.
• Active Voice Structure: Always follows the pattern Subject + Verb + Object. For Simple Present, it is Subject + V1 (s/es) + Object.

The correct answer is Option 1.

 

Key Points

• The main verb in the sentence is clarified, which is in the past tense.
• According to the sequence of tenses, if the principal clause is in the past tense, the subordinate clause should also be in the past tense.
• The original phrase uses are disbursed (present tense), which is grammatically inconsistent with the reporting verb clarified.
• The correct form should be were disbursed to maintain tense consistency throughout the sentence.
• The adverb judiciously correctly modifies the verb disbursed, and not misused maintains a parallel structure.

Therefore, the correct answer is Option 1.

 

Correct Sentence: 'The minister clarified that the funds allocated for the scheme were disbursed judiciously and not misused as it has been alleged.'

 

Additional Information

• Option 2: 'were disbursed with judiciousness and not misused' is grammatically possible but more wordy than using the adverb judiciously.
• Option 3: 'were not misused and had been disbursed in judiciously' is incorrect because in judiciously is an ungrammatical combination of a preposition and an adverb.
• Option 4: 'No improvement required' is incorrect because the present tense are must be changed to the past tense were to match the main verb clarified.

The correct answer is 'of'.

 

Key Points

• The verb dream is commonly followed by the preposition of (or about) when it means to contemplate or imagine a future possibility, desire, or aspiration.
• In the given sentence, dreamed of going correctly expresses the children's wish to visit the water park with their superhero.
• The preposition of links the verb dreamed with the gerund phrase going to the water park.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'The children dreamed of going to the water park with their superhero.'

 

Additional Information

• Option 1 (for): This is incorrect because we do not use the structure 'dream for doing something'; instead, verbs like 'hope' or 'long' are used with 'for'.
• Option 4 (in): This is incorrect because 'dream in' is typically used to specify a medium or state (e.g., 'dream in color' or 'dream in French'), which does not fit the context of the sentence.

The correct answer is Option 4.

Key Points

• The paragraph follows a chronological narrative regarding the arrest and investigation of Aksionov, eventually leading to his trial.
• Sentence C is the first sentence after S1 as it depicts the immediate action following the police officer’s order to bind him:
• 'As they tied his feet together and flung him into the cart, Aksionov crossed himself and wept.'
• Sentence A follows because it describes the subsequent steps taken by the authorities—confiscating his property and moving him to a place of detention:
• 'His money and goods were taken from him, and he was sent to the nearest town and imprisoned there.'
• Sentence B is the third sentence as the focus shifts to the background investigation conducted during his imprisonment:
• 'Inquiries as to his character were made in Vladimir.'
• Sentence D is the fourth sentence as it provides the specific feedback from the merchants and inhabitants of Vladimir (referred to as ‘that town’) regarding his past behavior:
• 'The merchants and other inhabitants of that town said that in former days he used to drink and waste his time, but that he was a good man.'
• This sequence leads perfectly into S2, which notes that after these preliminary events, the trial officially began.
• The correct sequence is CABD.

Coherent paragraph after rearrangement:

'The police officer ordered the soldiers to bind Aksionov and to put him in the cart. As they tied his feet together and flung him into the cart, Aksionov crossed himself and wept. His money and goods were taken from him, and he was sent to the nearest town and imprisoned there. Inquiries as to his character were made in Vladimir. The merchants and other inhabitants of that town said that in former days he used to drink and waste his time, but that he was a good man. Then the trial came on: he was charged with murdering a merchant from Ryazan and robbing him of twenty thousand Rubles.'